Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1

The Littlest Higgs model with T-parity (LHT) belongs to the simplest new physics scenarios with new sources of flavour and CP violation. The latter originate in the interactions of ordinary quarks and leptons with heavy mirror quarks and leptons that are mediated by new heavy gauge bosons. Also a heavy fermionic top partner is present in this model which communicates with the SM fermions by means of standard (Formula presented.) and (Formula presented.) gauge bosons. We present a new analysis of quark flavour observables in the LHT model in view of the oncoming flavour precision era. We use all available information on the CKM parameters, lattice QCD input and experimental data on quark flavour observables and corresponding theoretical calculations, taking into account new lower bounds on the symmetry breaking scale and the mirror quark masses from the LHC. We investigate by how much the branching ratios for a number of rare K and B decays are still allowed to depart from their SM values. This includes (Formula presented.) , (Formula presented.) , (Formula presented.) , (Formula presented.) , (Formula presented.) , (Formula presented.) , (Formula presented.) , and (Formula presented.). Taking into account the constraints from (Formula presented.) processes, significant departures from the SM predictions for (Formula presented.) and (Formula presented.) are possible, while the effects in B decays are much smaller. In particular, the LHT model favours (Formula presented.) , which is not supported by the data, and the present anomalies in (Formula presented.) decays cannot be explained in this model. With the recent lattice and large N input the imposition of the (Formula presented.) constraint implies a significant suppression of the branching ratio for (Formula presented.) with respect to its SM value while allowing only for small modifications of (Formula presented.). Finally, we investigate how the LHT physics could be distinguished from other models by means of indirect measurements and discuss the consequences for quark flavour observables of not finding any LHT state in the coming years.